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Theorem simprll 489
Description: Simplification of a conjunction. (Contributed by Jeff Hankins, 28-Jul-2009.)
Assertion
Ref Expression
simprll ((𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)) → 𝜓)

Proof of Theorem simprll
StepHypRef Expression
1 simpl 102 . 2 ((𝜓𝜒) → 𝜓)
21ad2antrl 459 1 ((𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)) → 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem is referenced by:  imain  4981  fcof1  5423  mpt20  5574  eroveu  6197  addcmpblnq  6463  mulcmpblnq  6464  ordpipqqs  6470  addcmpblnq0  6539  mulcmpblnq0  6540  nnnq0lem1  6542  prarloclemcalc  6598  addlocpr  6632  distrlem4prl  6680  distrlem4pru  6681  ltpopr  6691  addcmpblnr  6822  mulcmpblnrlemg  6823  mulcmpblnr  6824  prsrlem1  6825  ltsrprg  6830  apreap  7576  apreim  7592  divdivdivap  7687  divmuleqap  7691  divadddivap  7701  divsubdivap  7702  ledivdiv  7854  lediv12a  7858  qbtwnz  9104  iseqcaopr  9216  leexp2r  9282  recvguniq  9567  rsqrmo  9599
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